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Global well-posedness of the Cauchy problem for certain magnetohydrodynamic-α models

✍ Scribed by Yi Du; Hua Qiu; Zhengan-Yao

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 247 KB
Volume: 33
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1265

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✦ Synopsis

This paper is devoted to study the Cauchy problem for certain incompressible magnetohydrodynamics-a model. In the Sobolev space with fractional index s>1, we proved the local solutions for any initial data, and global solutions for small initial data. Furthermore, we also prove that as a → 0, the MHD-a model reduces to the MHD equations, and the solutions of the MHD-a model converge to a pair of solutions for the MHD equations.

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## Abstract This paper is devoted to the study of the Cauchy problem of incompressible magneto‐hydrodynamics system in the framework of Besov spaces. In the case of spatial dimension __n__⩾3, we establish the global well‐posedness of the Cauchy problem of an incompressible magneto‐hydrodynamics sys